Fig. 1: Comparison between the conventional BFA and the unconventional BFA.
a Dispersion diagram near the 2D Dirac point (DP), obtained with the PT symmetric Hermitian Hamiltonian \(H={f}_{x}{\sigma }_{1}+{f}_{y}{\sigma }_{3}\). Re(ω) denotes the real part of eigenvalues as a function of fx and fy for the two eigenvalues in orange and blue, respectively. b Paired second-order exceptional points (EP2, red dots) obtained from splitting the DP by introducing gain and loss term \(qi{\sigma }_{3}\) to the Dirac Hamiltonian (\({\sigma }_{1 \sim 3}\) denote Pauli matrices), where q is the perturbation term. The paired EP2s are stably connected by the conventional bulk-Fermi-arc (BFA). The eigenvalues on the conventional BFA are conjugate to each other (real parts coalescence). c Dispersion diagram near the defective triple point (DTP) on the 2D parameter space. The red lines denote ELs, and the DTP is embedded in the ELs. The three real eigenvalues are marked in orange, blue, and green, respectively. d Paired EP3s obtained from splitting the DTP by introducing perturbations with symmetries preserved. EP3s are both cusps of ELs, which are stably connected by the unconventional BFA residing in the broken phase domain. The three eigenvalues on the unconventional BFA share identical real parts and have different imaginary parts. Two of the three eigenvalues on the unconventional BFA are conjugate to each other, while the other eigenvalue is real.
